Geophysical data processing technique



April 7', 1970 c, ccLu EI'AL 3,504,974

GEOPHYSICAL DATA PROCESSING TECHNIQUE 2 Sheets-Sheet 1 Filed June 22. 1966 MONOCHROMATIC RADIATION RECORDER I06 OUTPUT SCENE FOURIER INPUT SCENE SOURCE PLANE I03 IOI FIG. 2

FIG.3

CARROLL D. MCCILURE FRANK J. Mc DONAL WILLIAM H. RUEHLE INVENTORS Wu) 6. W

ATTORNEY April 7, 1970 I c. o; M CLURE ETAL 3,504,974

GEOPHYSICAL DATA PROCESSING TECHNIQUE Filed June 22. 1966 3 Sheets-Sheet 2 FIG. 6

FIG. 5

FIG. 7

CARROLL'D. McC'LURE FRANK J. McDONAL WILLIAM H. RUEHLE INVENTORS ATTORNEY United States Patent 3,504,974 GEOPHYSICAL DATA PROCESSING TECHNIQUE Carroll D. McClure, Frank J. McDonal, and William H.

Ruehle, Dallas, Tex., assignors to Mobil Oil Corporation, a corporation of New York Filed June 22, 1966, Ser. No. 559,462 Int. Cl. G06k 9/08; G01v 1/00 US. Cl. 356-71 4 Claims ABSTRACT OF THE DISCLOSURE This invention relates to a technique for processing two dimensional data, such as magnetic or gravity data measured by selective sampling along a given surface area, and more particularly to the processing of such data in a computer of the optical type.

In the past, magnetic and gravity data in two dimensional form have been processed and filtered in computers of the analog and digital type. Processing in this manner, however, can be expensive as well as relatively time consuming.

In accordance with the present invention, sampled geophysical data obtained from measurements carried out spatially in two dimensions are applied to an optical computer whereby processing may be carried out rapidly and economically for the production of records which may be analyzed visually for sought-after information.

In carrying out the present invention, the measurements are obtained at selected spaced-apart sampling intervals. From the resulting measurements there is produced a reduced size variable density light transparency representation of the two dimensional sampled data. This representation is applied to the computer to form therein a diffraction pattern which defines the frequency spectrum of the data. The frequency spectrum is operated on to perform a desired filtering action to produce a resultant function which then is recorded.

In the embodiment disclosed, the frequency spectrum is operated on by an operator to produce in the output plane a scene which, when recorded, is of the variable density form representative of smooth and continuous variations of characteristics of the two dimensional geophysical pa'ameter sampled.

For further objects and advantages of the present invention and for a more complete understanding thereof, reference may now be had to the following detailed description taken in conjunction with the accompanying drawings wherein:

FIGURE 1 illustrates an optical computer for carrying out the present invention;

FIGURE 2 illustrates two dimensional sampled data obtained for processing;

FIGURE 3 illustrates a record of the output data as obtained with the computer of FIGURE 1 in accordance with one aspect of the present invention;

FIGURE 4 illustrates a variable density representation of the data of FIGURE 2;

3,504,974 Patented Apr. 7, 1970 FIGURE 5 illustrates an operator which may be employed in the computer for processing the data;

FIGURE 6 illustrates characteristics of the operator of FIGURE 5; and

FIGURE 7 illustrates the result of a step in processing the sampled data of FIGURE 2 for obtaining the variable density representation of FIGURE 4.

Referring now to FIGURE 1, there will be described the computer employed for carrying out the present invention. The computer shown is of the well-known optical type and comprises a monochromatic light source including suitable lenses for directing monochromatic light toward an input scene illustrated at 101. A spherical lens 102 is employed for focusing the light from the input scene. The Fourier plane is illustrated at 103. A second spherical lens 104 is employed for collimating the light toward an output scene, illustrated at 105, and a recorder 106, the latter of which may comprise a camera. The input scene 101, spherical lens 102, Fourier plane 103, spherical lens 104, and output scene 105 are aligned and spaced according to well-established optical formulas so that the diffraction pattern of 101 is sharply focused at 103 and the image of 101 is sharply focused at 105.

The computer disclosed is employed for processing and filtering two dimensional geophysical data obtained from two dimensional measurements, for example, of gravity or magnetic fields of interest or, for example, from measurements of the earths surface temperature, etc. In obtaining the data for use in the computer, sampling measurements over the area of interest may be carried out at points spaced apart in two dimensions forming a grid pattern as illustrated in FIGURE 2, or, of example, in a continuous manner along each of a series of spaced-apart lines. The resulting data are processed to form a reduced size variable density representation which is applied as the input scene of the computer. The data obtained from sampling may be employed directly to produce the input scene or may be employed to produce maps from which the input scene may be derived. FIGURE 4 illustrates an enlargement of one form of a variable density representation produced from the data for use as the input scene. A characteristic of the sampled data is operated on preferably by placing a filter function in the Fourier plane of the computer to carry out, in the spatial frequency domain, multiplication of the filter function with the spatial frequency spectrum of the input scene. This results in the production at the output plane of a scene, which when recorded may be of the variable density type as illustrated in FIGURE 3. This output scene represents smooth and continuous variations of the potential of the sampled field. Preferably, the filter function employed has desirable filtering characteristics which allow other filtering operations to be performed. The output scene recorded can be analyzed visually for sought-after information or may be operated on further, for example, by scanning with a conventional scanning system for the production of a contour map.

Referring again to FIGURE 2, there will be described one technique of particular interest for sampling the potential fields for the production of a desired variable density representation employed in the: computer. The numbers in FIGURE 2, represent the amplitude, for eX- ample, of the gravity or magnetic potential as measured at stations forming a grid pattern over a surface area or terrain of interest. Measurements are carried out at the stations located at the intersection of columns designated A-K, respectively, and rows designated at LS. The distance selected between measuring stations may be expressed in the following manner and is selected in accordance with the sampling theorem, so that wherein:

A is the distance between measuring stations along the rows and columns, and

f is the highest measurable spatial frequency expected in the field sampled. By spatial frequency is meant the rate at which the amplitude of the samples varies with the distance and thus has the dimensions of l/ distance.

As mentioned previously, the sampled data are converted to a reduced size variable density representation, one embodiment being illustrated in FIGURE 4. This representation comprises an opaque or substantially opaque mask 110 having a plurality of openings 111, each extending therethough at a position corresponding to a given sampling station. The transmission of light through each opening is proportional to the amplitude of the measurement obtained at the corresponding station.

In processing the representation of FIGURE 4, the reduced size variable density representation produced is placed in the input plane of the computer. Light from the source 100 is passed through the variable density representation and through lens 102 to form a diffraction pattern in the Fourier plane which defines the spatial frequency spectrum of the input scene. Thus, the Fourier transform is obtained in the Fourier plane which, in the present case, is a two dimensional transform. The amplitude spectrum consists of the amplitude spectrum of the field sampled forming a primary component at frequencies from plus complimentary components at high frequencies. Smoothing may be carried out by employing in the Fourier plane a filter function comprising an opaque mask, illustrated at 120 in FIGURE 5, and having a square or rectangular aperture 121 extending therethrough. The dimensions of the sides of the aperture 121 are sufficient to allow passage of spatial frequencies within a range extending from Hence, the higher frequencies are blocked and smoothing or interpolation of the samples is carried out whereby the output scene when recorded is the two dimensional continuous representation shown in FIGURE 3.

In the optical system employed, the dimensions of the sides of the aperture 121 are equal to 2Lf 'y, wherein:

f is the highest measurable spatial frequency expected in the field sampled;

L is the focal length of the lens 102; and

is the wave length of the light from source 100.

A continuous filtered scene may be obtained by employing a desired filter, illustrated at 122 in FIGURE 5 in the aperture 121 to perform within the spatial frequency range of for example, high pass, low pass, band pass filtering, or, for example, second derivative operations to obtain the curvature of the gravity or magnetic fields measured. The particular filter employed in the aperture 121 of the mask 120 of FIGURE 5 performs high pass filtering operations, and is a variable density transparency. The curve X of FIGURE 6 illustrates the variation of the transmittance of the filter to light. The abscissa represents distance extending from the center of the filter at 0, while the ordinate represents transmittance. It is to be understood that the other types of filters which may be employed, such as low pass or band pass, preferably will be of the variable density type also. Variable density filters are preferred rather than sharp cutoff filters in order to avoid interfering undulations which may otherwise be produced in the output.

In one embodiment, the variable density representation of FIGURE 4 may be obtained by converting the sampled data of FIGURE 2 to spots, as illustrated at in FIGURE 7. Each spot will have a density dependent upon the amplitude of the measurement obtained at the correspondent station. Each spot may comprise a circle having a given number of dots, as illustrated by the enlargement at 131 of FIGURE 7. The number of dots in each circle is proportional to the amplitude of the measurement obtained at the corresponding station. The spots are photographed and the resulting negative reduced in size for use in the computer.

In a further embodiment, the light transparency variable density representation for use as the input scene may be produced from a contour map drawn from sampled data, for example, from that of FIGURE 2. Each selected contour interval will be assigned a density corresponding to the average value of the sampled data found between the contour lines. The dot process described in connection with FIGURE 7 may be employed to obtain the desired density for each contour interval. The representation then may be photographed and the resulting negative reduced in size and employed as the input scene. The reduced-sized negative will comprise a mask having contour intervals of different light transparency. Light transmitted through each interval will be proportional to the magnitude of the average value of the corresponding sampled data.

Having described the invention, it will be understood that modifications may now suggest themselves to those skilled in the art, and it is intended to cover all those which fall Within the scope of the appended claims.

What is claimed is: 1. A method of obtaining and processing geophysical data comprising the steps of:

spatially measuring in two dimensions, at spaced-apart measuring positions, a parameter of a geophysical field of interest, from the measurement obtained from said spaced-apart positions, producing an input comprising a twodimensional mask having a plurality of variable density light transparency areas which extend in two dimensions and are spaced apart from each other, each area corresponding to one of said measuring positions, the transmission of light through each area being dependent upon the parameter measured at the corresponding measuring position, inserting said input into the input plane of an optical device having a source of monochromatic light, an input plane, a Fourier plane, and an output plane, inserting an optical filter in said Fourier plane to perform a desired filtering operation on the data represented by said input, and recording the output produced by said device when said light source is operated to transmit light through said variably density light transparency areas of said input and through said filter to said ouput plane. 2. The method of claim 1 wherein the step of measuring includes:

measuring said parameter of said geophysical field of interest at positions forming a grid pattern over a surface area of interest, the distance A between adjacent measuring positions along the rows and columns of the grid being defined as:

wherein:

f is the highest measurable spatial frequency expected in the field measured. 3. The method of claim 2 wherein said filtering oper- 7 5 ation includes:

allowing the passage of spatial frequencies within a range from and blocking the passage of higher spatial frequencles.

4. A method of obtaining and processing geophysical data comprising the steps of:

spatially measuring in two dimensions within a predetermined area at spaced-apart measuring positions the magnitude of a geophysical field of interest,

from said measurements obtained from said spacedapart measuring positions, producing an input comprising a two-dimensional mask having a plurality of variable density light transparency contour intervals which extend in two dimensions,

the density of said contour intervals at different positions in both of said dimensions being dependent upon the magnitude of said geophysical field at corresponding positions within said area in which said measurements are obtained,

inserting said input into the input plane of an optical device having a source of monochromatic light, an input plane, a Fourier plane, and an output plane,

inserting a filter in said Fourier plane to perform a desired filtering operation on the data represented by said input, and

recording the output produced by said device when said light source is operated to transmit light through said variable density light transparency contour intervals of said input and through said filter to said output plane.

References Cited OTHER REFERENCES Trabka, Image Transformations J.O.S.A., v. 54, 20 No. 10, Oct, 1964, pp. 1242-1255, (88/1-OSR).

Jackson, Analysis of Variable Density Seismograms Geophysics, v. xxx, No. 1, Feb, 1965, pp. 5-23, (88/1-OSR).

25 JEWELL H. PEDERSEN, Primary Examiner W. A. SKLAR, Assistant Examiner US. Cl. X.R. 

